Significance level for a hypothesis test for a linear regression
Consider linear regression model , where are unknown and , are iid, normally distributed with mean =0 and variance =9. Consider the hypothesis with the alternative , with the critical region , where b^ is a maximum likelihood estimator and c is chosen in such a way that the significance level of a test is equal to 0,05. Calculate c.
Could you help me with this exercise? It is taken from the actuary exam organized in my country. I thought that I am able solve this exercise, however my answer c=0,7528 is wrong, the correct answer is c=1,47.
Edited: the exercise seems very easy, but I'm sure that my method of solution is wrong, as I've seen the similar exercise and my method results with the wrong answer as well.
That's why I've decided to start a bounty, however I do not know how (I can see "question eligible for bounty in 59 minutes" only, not "start a bounty")